In recent years, there have been proposed and developed various combustion control technologies in fuel injection engine systems capable of executing a split fuel injection mode suitable for a rapid exhaust temperature rise, for example in presence of a request for rapid activation of catalyst. One such combustion control system with split fuel injection system interaction has been disclosed in Japanese Patent Provisional Publication No. 2000-320386 (hereinafter is referred to as “JP2000-320386”). In the Diesel-engine fuel injection control system disclosed in JP2000-320386, in presence of a request for a catalyst bed temperature rise, the fuel injection control system executes a split fuel injection mode in which a basic amount of fuel, determined based on a required engine torque, is sprayed or injected thrice separately by way of three-split fuel injection near top dead center (TDC) on the compression stroke. During the split fuel injection mode, if necessary, the fuel injection amount is increasingly compensated for.